Decoding lower-limb motor imagery (MI) is highly important in brain‒computer interfaces (BCIs) and rehabilitation engineering. However, it is challenging to classify lower-limb MI from electroencephalogram (EEG) signals, because lower-limb motions (LLMs) including MI are excessively close to physiological representations in the human brain and generate low-quality EEG signals. To address this challenge, this paper proposes a multidimensional attention-based convolutional neural network (CNN), termed MACNet, which is specifically designed for lower-limb MI classification. MACNet integrates a temporal refining module and an attention-enhanced convolutional module by leveraging the local and global feature representation abilities of CNNs and attention mechanisms. The temporal refining module adaptively investigates critical information from each electrode channel to refine EEG signals along the temporal dimension. The attention-enhanced convolutional module extracts temporal and spatial features while refining the feature maps across the channel and spatial dimensions. Owing to the scarcity of public datasets available for lower-limb MI, a specified lower-limb MI dataset involving four routine LLMs is built, consisting of 10 subjects over 20 sessions. Comparison experiments and ablation studies are conducted on this dataset and a public BCI Competition IV 2a EEG dataset. The experimental results show that MACNet achieves state-of-the-art performance and outperforms alternative models for the subject-specific mode. Visualization analysis reveals the excellent feature learning capabilities of MACNet and the potential relationship between lower-limb MI and brain activity. The effectiveness and generalizability of MACNet are verified.